What is the integral of cos^2(x+pi/2) ?

The integral of cos^2(x+pi/2) is 1/2 (x-1/2 sin(2x))+C

Popular >

integral of cos^2(x+pi/2)

\int cos^{2} (x + \frac{π}{2}) d x

\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

Solution steps

\int cos^{2} (x + \frac{π}{2}) d x

Rewrite using trig identities

= \int \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d x - \int cos (2 x) d x)

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

= \frac{1}{2} (x - \frac{1}{2} sin (2 x))

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

y = 6 x e^{x}, (0, 0)

\int 14 x 7 x - 3 d x

\frac{d}{d x} (e^{5 x s i n (2 x)})

\int 5 cos (x) + 3 sin (x) d x

f (x) = 2 x^{2} + 8 x

What is the integral of cos^2(x+pi/2) ?
The integral of cos^2(x+pi/2) is 1/2 (x-1/2 sin(2x))+C